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Simplifying 0 = 2x2 + 3x2 + -12x + 1 Reorder the terms: 0 = 1 + -12x + 2x2 + 3x2 Combine like terms: 2x2 + 3x2 = 5x2 0 = 1 + -12x + 5x2 Solving 0 = 1 + -12x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 12x + -5x2 = 1 + -12x + 5x2 + -1 + 12x + -5x2 Reorder the terms: -1 + 12x + -5x2 = 1 + -1 + -12x + 12x + 5x2 + -5x2 Combine like terms: 1 + -1 = 0 -1 + 12x + -5x2 = 0 + -12x + 12x + 5x2 + -5x2 -1 + 12x + -5x2 = -12x + 12x + 5x2 + -5x2 Combine like terms: -12x + 12x = 0 -1 + 12x + -5x2 = 0 + 5x2 + -5x2 -1 + 12x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -1 + 12x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -2.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -2.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -2.4x + x2 = 0 + -0.2 -2.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -2.4x + x2 = -0.2 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.2 + 1.44 Combine like terms: -0.2 + 1.44 = 1.24 1.44 + -2.4x + x2 = 1.24 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + -1.2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + -1.2 = 1.113552873 Simplifying x + -1.2 = 1.113552873 Reorder the terms: -1.2 + x = 1.113552873 Solving -1.2 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.113552873 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.113552873 + 1.2 x = 1.113552873 + 1.2 Combine like terms: 1.113552873 + 1.2 = 2.313552873 x = 2.313552873 Simplifying x = 2.313552873Subproblem 2
x + -1.2 = -1.113552873 Simplifying x + -1.2 = -1.113552873 Reorder the terms: -1.2 + x = -1.113552873 Solving -1.2 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.113552873 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.113552873 + 1.2 x = -1.113552873 + 1.2 Combine like terms: -1.113552873 + 1.2 = 0.086447127 x = 0.086447127 Simplifying x = 0.086447127Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.313552873, 0.086447127}
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